use the newton-raphson method to find an approximate value of 3√7 . use the method until successive approximations obtained by calculator are identical. an appropriate function to use for the approximation would be f (x) = A x^2 + B x^3 + C x + D where A= B= C= D=
If c1 = 2, then c2 = ___
2√3= ____

Answers

Answer 1
First, let's find the function to use for the Newton-Raphson method approximation. We want to find an approximation of 3√7, so we can use f(x) = x^3 - 7 and rewrite it as f(x) = -7 + x^3.

Setting A = B = C = D = 0 in the given function, we get f(x) = x^3 - 7.

Next, we apply the Newton-Raphson method with x1 = 2, which gives us:

x2 = x1 - f(x1) / f'(x1)
x2 = 2 - (2^3 - 7) / (3 * 2^2)
x2 = 2 - (8 - 7) / 12
x2 = 2 - 1/12
x2 = 23/12

Next, we apply the Newton-Raphson method again with x2, which gives us:

x3 = x2 - f(x2) / f'(x2)
x3 = 23/12 - ((23/12)^3 - 7) / (3 * (23/12)^2)
x3 = 23/12 - (12167/20736 - 7) / (3 * 529/144)
x3 = 23/12 - (4337/15552) / (529/48)
x3 = 23/12 - (36/15552)
x3 = 2783/1440

We can continue this process of applying the Newton-Raphson method until we obtain successive approximations that are identical. However, we can stop here and use 2783/1440 as our approximate value for 3√7.

Converting to a decimal approximation, we get:

3√7 ≈ 2.660874...

Rationalizing the denominator, we get:

3√7 ≈ (2783√21) / 1440

Therefore, our final answer is 2√3 = (2 * √3) ≈ 3.464.

Related Questions

Question 4(Multiple Choice Worth 2 points)
(Irrational Numbers MC)
Order √50,-7.1.3-7 from least to greatest.
0 -7.1.-7. √50,23
O
0-71.-7.7.23,√50
O
0 -7.1.-723√50
0-7-7.1,√50,23

Answers

Answer:

D

Step-by-step explanation:

The square root of 50 is approximately equal to 7.07

-7.1111… can be rounded to -7.11

23/3 is equal to approximately 7.67

-7 1/5 is equal to -7.2

Write 735 as the product of its prime factor.

Answers

Answer:

[tex]735 = 3 \times 5 \times {7}^{2} [/tex]

Step-by-step explanation:

[tex]735 = 7 \times 105[/tex]

[tex]735 = 7 \times 3 \times 35[/tex]

[tex]735 = 7 \times 3 \times 5 \times 7[/tex]

[tex]735 = 3 \times 5 \times {7}^{2} [/tex]

i have a small area that i want to place 2 bench press machines. how much room will i need to reserve for those?

Answers

To place two bench press machines in a small area, you will need a space of approximately 10 feet by 10 feet. Let's discuss it in detail below. Here are the dimensions of the bench press machine, which can help determine the amount of space required to fit two bench press machines in a small area:

The length of the bench press machine is between 48 inches and 54 inches.

The width of the bench press machine is between 28 inches and 32 inches.

The height of the bench press machine is between 48 inches and 56 inches.

Based on the above dimensions of the bench press machine, two machines can be placed in a small area of 10 feet by 10 feet. However, for safe use, the following guidelines should be followed:

There should be at least 6 feet of distance between the two bench press machines. There should be at least 3 feet of clearance in the front of the bench press machine to allow for safe movement during exercises. There should be at least 2 feet of clearance behind the bench press machine to allow for a safe exit in case of an emergency.

Thus, to place two bench press machines in a small area, you will need a space of approximately 10 feet by 10 feet.

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Xavier buys a dog collar that costs $6.79. He pays for the dog collar
with a $10 bill.
How much change does Xavier receive?

Answers

Answer: Xavier will receive $3.21 in change.

Step-by-step explanation:

To find the change Xavier receives, we need to subtract the cost of the dog collar from the amount he paid with his $10 bill:

Change = $10 - $6.79 = $3.21

Therefore, Xavier will receive $3.21 in change.

HELP DUE TODAY!!!!!!!!!
. Write the (x, y) coordinates for P in terms of cosine and sin.
6. Using the image above, if cos(Θ) = 0.6, what are the coordinates of P? Explain your reasoning.

Answers

Answer:   (0.6,  -0.8)

Explanation:

Use the pythagorean trig identity to determine sine based on cos(theta) = 0.6

[tex]\sin^2(\theta)+\cos^2(\theta) = 1\\\\\sin^2(\theta)=1-\cos^2(\theta)\\\\\sin(\theta)=\pm\sqrt{1-\cos^2(\theta)}\\\\\sin(\theta)=-\sqrt{1-\cos^2(\theta)} \ \ \text{....sine is negative in quadrant Q4}\\\\\sin(\theta)=-\sqrt{1-(0.6)^2}\\\\\sin(\theta)=-\sqrt{1-0.36}\\\\\sin(\theta)=-\sqrt{0.64}\\\\\sin(\theta)=-0.8\\\\[/tex]

Since [tex]\cos(\theta)=0.6 \text{ and } \sin(\theta)=-0.8[/tex], the location of point P is (0.6, -0.8)

Recall that for any point (x,y) on the unit circle, we have:

[tex]\text{x}=\cos(\theta)\\\\\text{y}=\sin(\theta)[/tex]

meaning cosine is listed first in any (x,y) pairing.

Pablo needs to memorize words on a vocabulary list for Latin class he has 12 words to memorize and he is 3/4 done how many words has Pablo memorized so far​

Answers

Answer:

9 words

Step-by-step explanation:

We know

He has 12 words to memorize, and he is 3/4 done.

How many words has Pablo memorized so far​?

We Take

12 x 3/4 = 9 words

So, Pable has memorized 9 words.

Determine wheter the given vale of the varible is a soultion of the equatiom1/3 h=6 h=2

Answers

No, the given value of h=2 is not a solution of the equation 1/3h=6.

We are given the equation:

1/3 h = 6

We need to determine whether h = 2 is a solution of this equation. To do this, we substitute h = 2 into the equation and see if it is true or not.

1/3 (2) = 6

2/3 = 6

This is not true, since 2/3 is not equal to 6. Therefore, h = 2 is not a solution of the equation 1/3 h = 6.

b) There are x number of books that worth Rs. 35 each and 5 books worth Rs. 30 each in a parcel prepared as a gift. The value of two such parcels is Rs. 580. i. Build up an equation using the above information. ii. Find the value of x by solving the equation.​

Answers

Answer:

Equation: 2(357+30×5) = 580

x=4

Step-by-step explanation:

In one package, there is such a relationship:

357+30X5 = y

(Y is the price of a package)

The price of two parcels is 580:

then. 24=580

y= 290

x=4, so: equation: 2(35x+150) =580

Step-by-step explanation:

A shopkeeper buys a number of books for Rs. 80. If he had bought 4 more for the same amount each book would have cost Rs. 1 less. How many books did he buy?

A

8

B

16

Correct Answer

C

24

D

28

Medium

Open in App

Updated on : 2022-09-05

Solution

Verified by Toppr

Correct option is B)

Let the shopkeeper buy x number of books. 

According to the given condition cost of x books =Rs80

Therefore cost of each book =x80

Again when he had brought 4 more books

Then total books in this case =x+4

So cost of each book in this case =x+480

According to Question, 

x80−x+480=1

x(x+4)80(x+4)−80x=1

x2+20x−16x−320=0

(x−16)(x+20)=0

x=16orx=−20

Hence the shopkeeper brought 16 books

URGENT PLEASE HELP!!
Given that f(x)=x^2+3x-7, g(x)=3x+5 and h(x)=2x^2-4, find each of the following. Solve each of the problems showing work.
f(g(x))
h(g(x))
(h-f) (x)
(f+g) (x)

Explain what method you used when had a squared term that had to be multiplied out.

Answers

For the given functions, f(x)=x²+3x-7, g(x)=3x+5 and h(x)=2x²-4, f(g(x))= 9x² + 30x + 33, h(g(x))= 18x² + 60x + 46, (h-f)(x)= x² - 3x + 3, (f+g)(x)= x² + 6x - 2.

Describe Function?

In mathematics, a function is a mathematical object that takes an input (or several inputs) and produces a unique output. It is a relationship between a set of inputs, called the domain, and a set of outputs, called the range.

Formally, a function f is defined by a set of ordered pairs (x, y) where x is an element of the domain, and y is an element of the range, and each element x in the domain is paired with a unique element y in the range. We write this as f(x) = y.

Functions can be represented in various ways, such as algebraic expressions, tables, graphs, or verbal descriptions. They can be linear or nonlinear, continuous or discontinuous, and may have various properties such as symmetry, periodicity, and asymptotic behavior.

To solve these problems, we substitute the function g(x) for x in f(x) and h(x) and simplify the resulting expressions.

f(g(x)):

f(g(x)) = f(3x+5) = (3x+5)² + 3(3x+5) - 7 (using the definition of f(x))

= 9x² + 30x + 33

h(g(x)):

h(g(x)) = h(3x+5) = 2(3x+5)² - 4 (using the definition of h(x))

= 18x² + 60x + 46

(h-f)(x):

(h-f)(x) = h(x) - f(x) = (2x² - 4) - (x² + 3x - 7) (using the definitions of h(x) and f(x))

= x² - 3x + 3

(f+g)(x):

(f+g)(x) = f(x) + g(x) = x² + 3x - 7 + 3x + 5 (using the definitions of f(x) and g(x))

= x² + 6x - 2

When multiplying out a squared term, such as (3x+5)², we can use the FOIL method, which stands for First, Outer, Inner, Last. We multiply the first terms, then the outer terms, then the inner terms, and finally the last terms, and then add up the results. For example:

(3x+5)² = (3x)(3x) + (3x)(5) + (5)(3x) + (5)(5)

= 9x² + 15x + 15x + 25

= 9x² + 30x + 25

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please help fast I am baffled

Answers

The expression for the number of non-adult sizes is s - 19.

What are expressions?

A value or amount is represented by an expression, which is a collection of numbers, variables, and mathematical operations like addition, subtraction, multiplication, and division. Calculations, complicated mathematical equations, and issues in a variety of disciplines, including science, engineering, economics, and statistics, may all be solved using expressions. Functions that depict a connection between variables, such as sin(x) and log(x), can also be included in expressions. Expressions are frequently employed to simulate real-world circumstances and provide predictions based on mathematical analysis.

Given that the total number od sweatshirts = s.

The number of non-adult sweatshirts can be calculated by:

Number of non-adult sizes = Total number of sweatshirts sold - Number of adult sizes

= s - 19

Hence, the expression for the number of non-adult sizes is s - 19.

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Find the measure of the last angle of the triangle below.
28⁰
35°

Answers

Measure of last angle of triangle is 117°

Triangle Properties

The triangle's characteristics include:

All triangles have a total of 180 degrees in their angles.The length of the longest two sides of a triangle is greater than the length of the third side.The length of the third side of a triangle is shorter than the difference between its two sides.Angle Sum Property

The angle sum property states that the sum of a triangle's three interior angles is always 180 degrees.

Angle of Triangle are

28° and 35°

Let the third angle be x

According to angle sum property

28°+35°+x=180°

x=117°

Measure of last angle of triangle is 117°

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The complete question is;

Find the measure of the last angle of the triangle below.

28⁰

35°

Image is attached below.

Fractions Questions 2

Answers

From what we are given we form the equation:

640×(1−2×3/8)

Cross out the common factor

Apply Multiplicative Distribution Law:

Cross out the common factor:

Calculate the product

Calculate the sum

Answer:
160

please help me with this savvas question!

Answers

Therefore, the compound inequality for the diameter of the washers is: 3.150 ≤ d ≤ 3.240.

What is inequality?

In mathematics, an inequality is a statement that compares two values or expressions, indicating that one is greater than, less than, or equal to the other. The symbols used to represent inequalities are:

">" which means "greater than"

"<" which means "less than"

"≥" which means "greater than or equal to"

"≤" which means "less than or equal to"

Inequalities can be solved by applying algebraic techniques, such as adding, subtracting, multiplying, or dividing both sides of the inequality by the same number. The solution to an inequality is a range of values that satisfy the inequality.

Here,

The formula for the circumference of a circle in terms of its diameter is:

C = πd

where π (pi) is approximately 3.14.

We are given that the acceptable range for the circumference of the washer is 9.9 ≤ C ≤ 10.2 centimeters. Substituting C = 3.14d into this inequality, we get:

9.9 ≤ 3.14d ≤ 10.2

Dividing all sides of the inequality by 3.14, we obtain:

3.15 ≤ d ≤ 3.24

Rounding to three decimal places, the corresponding interval for the diameters of the washers is:

3.150 ≤ d ≤ 3.240

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D. On désire connaître la quantité de moulure dont on a besoin pour encadrer un tableau. Aire ou Périmètre​

Answers

Answer:

Step-by-step explanation:

Perimeter

Pls mark me brainliest

A baseball is thrown straight upwards from the ground and undergoes a free fall motion as it rises towards its highest point. What changes, if any, would be observed of the velocity and the acceleration of the baseball as it rises towards its highest point? Pick two answers.

The velocity increases.

The velocity decreases.

The velocity remains a constant value.

The acceleration increases.

The acceleration decreases.

The acceleration remains a constant value

Answers

The baseball thrown upwards will experience a change in its velocity while its acceleration will be constant.

A type of motion known as upward motion involves an item moving up against the pull of gravity.

The opposing force of gravity causes an object to go upward with a decreasing vertical velocity as it does so. When the item reaches its maximum height, its velocity ultimately zeroes out. The velocity starts to rise as the object starts to descend and eventually reaches its highest point just before impact with the ground.

The object's acceleration during its upward motion is constant and always points downward. Hence, it follows that an item moving upwards will experience a change in velocity but not in acceleration.

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She begins at sea level, which is an elevation of 0 feet.
She descends for 50 seconds at a speed of 5 feet per second.
She then ascends for 54 seconds at a speed of 4.4 feet per second.

Answers

Answer:

The diver descends:

50 seconds x 5 feet/second = 250 feet

The diver ascends:

54 seconds x 4.4 feet/second = 237.6 feet

Therefore, the total change in elevation is:

250 feet (descent) - 237.6 feet (ascent) = 12.4 feet

So, the diver's final elevation is:

0 feet (starting elevation) - 12.4 feet (change in elevation) = -12.4 feet

Therefore, the diver ends up 12.4 feet below sea level.

Answer:

it is 1

Step-by-step explanation:

its is 1 2 3 hsvs jafsnsjhd jsusgsmsi jshsbjdg

Your teacher prepares a large container full of colored

beads. She claims that 1/8 of the beads are red, 1/4 are

blue, and the remainder are yellow. Your class will take a

simple random sample of beads from the container to test the teacher's claim. The smallest number of beads you

can take so that the conditions for performing inference

are met is.

15

16

30

40

90

Answers

The smallest number of beads we can take so that the conditions for performing inference are met is 40.

Probability:

The probability of an event is a number that indicates the probability of the event occurring. Expressed as a number between 0 and 1 or as a percent sign between 0% and 100%. The more likely an event is to occur, the greater its probability. The probability of an impossible event is 0; the probability of a certain event occurring is 1. The probability of two complementary events A and B - A occurring or B occurring - adds up to 1.

According to the Question:

Given in the question,

Teacher prepares a large container filled with colored beads. She claims that 1/8 beads are red, 1/4are blue, and the rest are yellow. Your class will test the teacher's claim by randomly drawing a simple sample of beads from the container.

Quadrant                     Frequency

      1                                    18

      2                                   22

      3                                   39

      4                                   21

The proportions are 1/8 , 1/4 and 5/8

Here, the smallest probability is 1/8 , thus it would be used to compute the frequency.

Now,

The expected frequencies are calculated as:

E = np₁ = 15 (1/8) = 1.875

E = np₂ = 16(1/8) = 2

E = np₃ = 30(1/8) = 3.75

E = np₄ = 40(1/8) = 5

E = np₅ = 80(1/8) = 10

Here, conditions are fulfilling for 40 and 90 but the smallest sample size is contained by 40. Thus, the correct option is 40.

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If the ratio a: b is 1 : 4 and the ratio b: c= 3:2, find the ratio (a + c) : c.

Answers

The required ratio of  is (a + c) : c 11:8.

How to find ratio ?

Given that a:b=1:4 and b:c=3:2.

We can simplify the ratio b:c by multiplying both sides by 4 to get b:c=12:8=3:2.

To find the ratio (a+c):c, we need to express a and c in terms of b. From the first ratio, we have [tex]a=\frac14 b$[/tex]. From the second ratio, we have [tex]c=\frac{2}{3}b$[/tex]. Substituting these values into the expression (a+c):c, we get:

[tex]$$(a+c):c = \left(\frac{1}{4}b + \frac{2}{3}b\right):\frac{2}{3}b$$[/tex]

Simplifying the expression inside the parentheses, we get:

[tex]$\frac{1}{4}b + \frac{2}{3}b = \frac{3b}{12} + \frac{8b}{12} = \frac{11b}{12}$$[/tex]

Therefore, the ratio [tex]$(a+c):c$[/tex] is:

[tex]$(a+c):c = \frac{11b}{12}:\frac{2}{3}b = 11:8$$[/tex]

Hence, the required ratio is 11:8$.

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A triangle has two sides of length 3 and 16. What is the largest possible whole-number length for the third side

Answers

The largest possible whole-number length for the third side is 18, which satisfies all three inequalities.

What is inequality theorem?

The triangle inequality theorem explains the relationship between the three sides of a triangle. This theorem states that for any triangle, the sum of the lengths of the first two sides is always larger than the length of the third side.

According to question:

Let x be the length of the third side. By the triangle inequality, we have:

3 + 16 > x and 16 + x > 3 and 3 + x > 16

Simplifying, we get:

19 > x and x > 13 and x < 19

The largest possible whole-number length for the third side is 18, which satisfies all three inequalities.

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If a certain apple tree grew 2 feet and then tripled its height, it would become 4 feet
shorter than the pine tree that grows on the other end of the street. Which
of the formulas below describes the relation between the height of the apple tree a
and the height of the pine tree p?

A) P-4=3a+2
B) P=2(a+3)+4
C) P=3(a+2)-4
D) P=3a+10

Answers

Answer:

Step-by-step explanation:

C.) P = 3(a+2)-4

The formula which describes the relation between the height of the apple tree and the height of the pine tree p is P=3(a+2)-4, the correct option is C.

What is a linear equation?

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

We are given that;

Growth of apple tree= 2feet

Now,

Let's call the original height of the apple tree "h". According to the problem, if the apple tree grew 2 feet and then tripled its height, it would become 4 feet shorter than the pine tree. So we can write:

3(h+2) - 4 = p

Simplifying, we get:

3h + 2 = p

Now we can see that option (D) P=3a+10 is very similar to our expression, but it has a constant term of 10 instead of 2. This constant term does not match the problem statement, which says that the apple tree would be 4 feet shorter than the pine tree, not taller. Therefore, option (D) is not the correct answer.

Option (A) P-4=3a+2 also does not match the problem statement. If we solve for p, we get:

P = 3a + 6

This means that the apple tree would be 6 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.

Option (B) P=2(a+3)+4 also does not match the problem statement. If we solve for p, we get:

P = 2a + 10

This means that the apple tree would be 10 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.

Option (C) P=3(a+2)-4 matches our expression from earlier. If we solve for p, we get:

P = 3a + 2

Therefore, by equation the answer will be P=3(a+2)-4.

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Write the first four terms of the sequence defined by a n = 5
{5, if n=1
a n -1 -5, if n>1

Answers

Answer:

The sequence is defined as follows:

a1 = 5

an = an-1 - 5, for n > 1

Using this definition, we can find the first four terms of the sequence as follows:

a1 = 5

a2 = a1 - 5 = 5 - 5 = 0

a3 = a2 - 5 = 0 - 5 = -5

a4 = a3 - 5 = -5 - 5 = -10

Therefore, the first four terms of the sequence are: 5, 0, -5, -10.

Write an equation for the line on a graph below.

Answers

Check the picture below.

Answer:

x=-3

Step-by-step explanation:

For each growth rate, find the associated growth factor.
1. 30% increase
2. 30% decrease
3. 2% increase
4. 2% decrease
5. 0.04% increase
6. 0.04% decrease
7. 100% increase

Answers

Answer:

The associated growth factor for a 30% increase is 1 + 0.30 = 1.30.

The associated growth factor for a 30% decrease is 1 - 0.30 = 0.70.

The associated growth factor for a 2% increase is 1 + 0.02 = 1.02.

The associated growth factor for a 2% decrease is 1 - 0.02 = 0.98.

The associated growth factor for a 0.04% increase is 1 + 0.0004 = 1.0004.

The associated growth factor for a 0.04% decrease is 1 - 0.0004 = 0.9996.

The associated growth factor for a 100% increase is 1 + 1 = 2.

Step-by-step explanation:

A growth factor is a multiplier that represents the amount by which a quantity changes as a result of a growth rate or percentage change. It is calculated by adding 1 to the decimal form of the growth rate. For example, if the growth rate is 30%, the decimal form is 0.30, and the growth factor is 1 + 0.30 = 1.30.

In case of a decrease, the growth factor is calculated by subtracting the decimal form of the decrease rate from 1. For example, if the decrease rate is 30%, the decimal form is 0.30, and the growth factor is 1 - 0.30 = 0.70.

In cases where the growth rate is a small percentage, it is important to convert it into a decimal by dividing the percentage by 100 before calculating the growth factor.

In the case of a 100% increase, the quantity doubles, so the growth factor is 2 (i.e., 1 + 1).

The table shows the number of hours spent studying for a history final exam and the score on that exam. Each row represents a single student. Which value is an outlier in the table below?
Exam Scores
Number of hours spent studying, x
Exam score
(out of 100), y
1.5
65
2
68
3.5
71
4.5
98
4.5
82
6
84
6.5
88
7
85
7
80
(1.5, 65)
(3.5, 71)
(4.5, 98)
(6.5, 88)

Answers

Answer:Given : number of hours spent studying for a history final exam and the score on that exam.

To Find : Which value is an outlier

(1.5, 65)

(3.5, 71)

(4.5, 98)

(6.5, 88)

Solution:

Number of hours spent studying =x            

Exam score   = y

x         y

1.5       65

2         68

3.5      71

4.5      98

6         82

1.5 -   2   difference = 0.5

2 - 3.5     difference = 1.5

3.5 - 4.5   difference = 1

4.5 - 6       difference = 1.5

No outlier

65  - 68   Difference  3

68 - 71      Difference  3

71 -  98      Difference  27

71 - 82     Difference  11

Hence 98 is outlier

(4.5    ,  98 )  is outlier

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Step-by-step explanation:

(HAZARD) Please help what graph represents Y=-2x+4 I will mark you the brainest

Answers

The graph of Y=-2x+4 should look like a downward sloping line that intersects the y-axis at 4.

What is intersect?

The term "intersect" typically refers to the point or points where two or more things, such as lines, curves, sets, or geometrical shapes, meet or cross each other. The intersection can be described as the common elements or properties shared by the different objects or sets that intersect.

According to question:

The graph of the equation Y=-2x+4 is a straight line with a slope of -2 and a y-intercept of 4. To graph this equation, you can use the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

To graph Y=-2x+4, follow these steps:

Plot the y-intercept at (0,4).To locate a different point on the line, use the slope of -2. To do this, move down 2 units and right 1 unit from the y-intercept. This gives you the point (1,2).Between the two points, doodle a straight line.

The graph of Y=-2x+4 should look like a downward sloping line that intersects the y-axis at 4.

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An amount of money is divided among A, B and C in the ratio 4: 7:9 A receives R500 less than C. Calculate the amount that is divided. ​

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Answer:

We know that A receives R500 less than C, so we can write:

4x = 9x - 500

Solving for x, we get:

5x = 500

x = 100

Now we can calculate the amounts received by each person:

A = 4x = 4(100) = R400

B = 7x = 7(100) = R700

C = 9x = 9(100) = R900

To check our answer, we can verify that the ratios of the amounts received by A, B, and C are indeed 4:7:9:

A:B = 400:700 = 4:7

B:C = 700:900 = 7:9

Therefore, the total amount divided is:

400 + 700 + 900 = R2000

So the amount that is divided is R2000.

Step-by-step explanation:

The total amount of money divided is R2000.

What is the ratio?

Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We are given that;

The ratio of A, B and C= 4:7:9

Now,

Let's start by assigning variables to the unknowns in the problem. Let's call the total amount of money "T". Then, if A receives 4x, B receives 7x, and C receives 9x, where "x" is some constant, we can write:

4x + 500 = C's share

We can also write an equation to represent the fact that the three shares add up to the total amount:

4x + 7x + 9x = T

Simplifying this equation, we get:

20x = T

Now we can substitute the first equation into the second equation and solve for x:

4x + 7x + (4x + 500) = 20x

15x + 500 = 20x

500 = 5x

x = 100

Now we can find the individual shares by multiplying x by the appropriate ratio factor:

A's share = 4x = 400

B's share = 7x = 700

C's share = 9x = 900

Finally, we can check that these add up to the total amount:

400 + 700 + 900 = 2000

Therefore, by the given ratio the answer will be R2000.

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Assume that head sizes (circumference) of new recruits in the armed forces can be approximated by a normal distribution with a mean 22.8 inches and standard deviation of 1.1 inches. Suppose a recruit was found with a head size of 23 inches Find the approximate Z-score for this recruit. a. 0 -0.18 b. 0.18 c. 0.96 d. 476.73

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The approximate Z-score for this recruit is b. 0.18.

The mean of the head sizes (circumference) of new recruits in the armed forces can be approximated by a normal distribution with a mean 22.8 inches and standard deviation of 1.1 inches. The head size of a recruit was found to be 23 inches.

The approximate Z-score for this recruit. The formula for Z-score is given by:

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

where X is the head size of the recruit, μ is the mean head size of recruits, and σ is the standard deviation of head sizes of recruits. Substituting the given values in the above formula, we get,

Z=(23-22.8)(1.1)

Z=0.2/1.1

Z [tex]\approx[/tex] 0.18

Thus, the approximate Z-score for this recruit is b. 0.18.

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If n(Ax B) = 72 and n(A) = 24, find n(B).

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Solving for Cartesian product n(B), we have n(B) = 72 / 24 = 3.

What is Cartesian product?

The Cartesian product is a mathematical operation that takes two sets and produces a set of all possible ordered pairs of elements from both sets.

In other words, if A and B are two sets, their Cartesian product (written as A × B) is the set of all possible ordered pairs (a, b) where a is an element of A and b is an element of B.

For example, if A = {1, 2} and B = {3, 4}, then A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}.

By the question.

We know that n (Ax B) represents the number of elements in the set obtained by taking the Cartesian product of sets A and B.

Using the formula for the size of the Cartesian product, we have:

n (Ax B) = n(A) x n(B)

Substituting the given values, we get: 72 = 24 x n(B)

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Determine if the ordered pair (-2, -4) is a solution for equation 2y - 3x = -2.

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Answer:

Step-by-step explanation:

2(-4) - 3(-2) = -2

 -8 + 6 = -2

   -2 = -2

The annual salaries (in $) within a certain profession are modelled by a random variable with the cumulative distribution function F(x)= {1−kx^−3 for x>44000 {0 otherwise, for some constant k. For these problems, please ensure your answers are accurate to within 3 decimals. a)Find the constant k here and provide its natural logarithm to three decimal places. b)Calculate the mean salary given by the model.

Answers

a) The constant k is 5.427 x 10^−12 and its natural logarithm is -26.68.

b) The mean salary of the given model by using the probability density function is approximately $270.86.

a) The cumulative distribution function of the given random variable is provided as follows:

F(x) = {1−kx^−3 if x>44000, and 0 otherwise

The cumulative distribution function is given as

F(x) = 1−kx^−3 if x>44000 and F(x) = 0, if x≤44000i)

We need to check the value of the cumulative distribution function at 44000

We have, F(44000) = 0

0 = 1−k(44000)^−3

⇒ 1 = k(44000)^−3

⇒ k = 1/(44000)^−3

⇒ 5.427 x 10^−12

Taking the natural logarithm of k, we have ln(k) = −28.68 (approx.)

Hence, the constant k is 5.427 x 10^−12 and its natural logarithm to three decimal places is -28.68

b) The probability density function is given as,

f(x) = F'(x) = 3kx^−4, for x>44000 and f(x) = 0, otherwise

The mean or expected value of the random variable is given as

E(X) = ∫[−∞,∞]xf(x)dx

= ∫[44000,∞]x(3kx^−4)dx

= 3k∫[44000,∞]x^−3dx

= 3k[(−1/2)x^−2] [∞,44000]

= (3k/2)(44000)^−2

= 270.86 (approx.)

Therefore, the mean salary given by the model is $270.86 (approx.)

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